In the past, an engine idle stop control device was proposed in PTL 1. This device brings a vehicle to an idling stop for purposes, for instance, of fuel consumption reduction when predetermined conditions are met. When braking force becomes smaller than the force of rolling backward on a gradient, this device detects the vehicle drawn down state and restarts an engine of the vehicle to inhibit the vehicle from rolling away.
Further, a braking force hold device was proposed in PTL 2. When a wheel speed pulse is input after a vehicle is brought to a standstill, this device detects a drawn down and starts an engine of the vehicle to inhibit the vehicle from rolling away.